Years ago, one of us delivered a class on sexism, presenting three of the most common ways society subtypes women: warm but incompetent, sexy but incompetent, and competent but cold. After class, two female students asked to meet privately and described a game called MFK that was played during the initial semester of their first year. Male students passed around a list of female peers, categorizing by what they would do to each: marry (warm but incompetent), the f-word (sexy but incompetent), or kill (competent but cold). The list was mysteriously leaked so that female students learned their place. The students wanted to know whether the research described in class had been inspired by the game. (We’ve since learned that this game is popular across universities.)

Whether explicitly (as in the MFK game) or more subtly communicated, subtyping undermines women in a classic divide-and-conquer strategy. Here’s how it plays out:

Each subtype cedes one — but only one — positive trait (warm, sexy, or competent), mixing flattery with derogation. Wholly negative stereotypes (competent and cold) would motivate anyone to resist. But it’s only human to want to maintain others’ good opinion on a positive trait (“At least they think I’m nice”) while trying to correct perceived deficits (“How can I convince them I’m smart?”). Even those of us who immediately see the game as disgusting are not immune to this urge to want to convince our community to both like and respect us.

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Subtyping inhibits women from banding together collectively in two ways. It motivates women to focus individually on trying to combat or compensate for their perceived flaws (rather than questioning the system that falsely assigns them). Eventually, many women acquiesce to these obstinate judgments, even embracing and identifying with their prescribed subtype, which inevitably results in competing tribes. It’s a racket that extorts power and unity, ultimately disempowering and dividing women.

And these divisions among women have been evident in some of the discussions about Harvey Weinstein’s abuses. Comments by designer Donna Karan, for which she has since apologized, implied that the sexy (but not smart) women should have known better than to go to that hotel room or dress so provocatively. “What are they asking for? Trouble.” We all know the accusation: Pretty women regularly trade on their looks to gain advantage with men, so they got what they deserve.

Mayim Bialik, who plays Amy on “The Big Bang Theory” and has a neuroscience PhD in real life, wrote about the pressures to accept the subtype the world places her in: smart, but not sexy or warm. In life, as well as on TV, she has been assigned to play “an androgynous, awkward, late bloomer . . . who loves science . . . and who sometimes wishes she were the hot girl.”

Of course, every subtype, by design, provides an incentive. Bialik notes, “I have also experienced the upside of not being a ‘perfect 10.’ As a proud feminist with little desire to diet, get plastic surgery, or hire a personal trainer, I have almost no personal experience with men asking me to meetings in their hotel rooms.”

Bialik has clarified that describing the careful strategies she takes to avoid harassment (“I dress modestly. I don’t act flirtatiously . . . ”) was in no way intended to blame women who dress less modestly for being harassed or assaulted. But the idea that only sexy women are harassed is itself an illusion. Research by Jennifer Berdahl, a gender scholar at the University of British Columbia, shows that, in many workplace settings, it’s “uppity” (i.e., ambitious and smart) women who get sexually harassed the most. They represent the most direct threat to the men who want to preserve male status and power. Humiliating and reducing ambitious women to sex objects cuts them down in an instant.

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Crucially, it’s not all or even most men who harass. The lie that “all men are like that” represents another damaging stereotype. It not only derogates men, but reinforces the idea that it’s useless to try to change things or hold men accountable — “It’s just locker room talk,” so we should ignore it.

But extraordinarily bad behavior by a few, permitted and covered up due to their power, has a chilling and divisive effect. The “competent women” strive to downplay their sexuality and learn when not to be “too smart.” The “sexy women” know they risk being blamed as provoking harassment if they speak up about it. The “warm women” know that calling out men who harass means giving up their one perceived positive trait, going from nice to nasty or shrill.

The “Me Too” movement has exposed the truth: All women are at risk and the victims are not at fault. It has also inspired a great show of unity among women, which itself is a clear sign that women are feeling more powerful. But all of us (both women and men) must reject and transcend the stereotypes that divide women into competing “types” as we band together to categorically reject harassment and bullying.

Amy Cuddy of Harvard University and Peter Glick of Lawrence University are social psychologists with expertise on gender. In collaboration with Susan Fiske, they have co-developed and extensively tested a warmth-competence model of stereotyping.